Pattern recognition method using fuzzy neuron

ABSTRACT

A method for determining whether a fuzzy symbol matches a predetermined reference pattern by generating membership functions that collectively represent a reference pattern having identifying features; sampling the fuzzy symbol to generate an input pattern representative of the fuzzy symbol; transforming the input pattern to generate an inverted input pattern; comparing the input pattern with a first membership function to determine a first quantity of identifying features of the reference pattern that are present in the fuzzy symbol; comparing the inverted input pattern with a second membership function to determine a second quantity of identifying features of the reference pattern that are present in the fuzzy symbol; and determining that the fuzzy symbol matches the reference pattern if the first and second quantities are sufficiently high.

This application is a continuation of U.S. application Ser. No.08/160,274 filed Dec. 2, 1993, now U.S. Pat. No. 5,434,930.

BACKGROUND OF THE INVENTION

a) Field of the Invention

The present invention relates to pattern recognition such as imagerecognition or voice recognition, and more particularly, is directed toa method of fuzzy-pattern-recognition by using a fuzzy neuron.

b) Description of the Related Art

As an information processing technique imitating information processingwithin a living body, a technique using a so-called neuron is known. Inthis technique, a learning function which the living body possesses isimitated in terms of software or hardware, and hence informationprocessing can be implemented in the form similar to the informationprocessing which is carried out within the human brain.

A fuzzy theory is known as a theory handling fuzzy information. In thistheory, a fuzziness which the information contains is represented bymembership functions. Since evaluation of the fuzziness is performed,the fuzzy theory can also be considered to be information processingsimilar to that which is carried out in, for example, the human brain.

A recent investigation has been directed toward the fusion of the fuzzytheory and the neuron. More specifically, so as to be able to recognizea pattern represented by fuzzy information, in other words, a patternsuch as a handwritten letter or a picture containing fuzziness, it isanticipated so combine the two such a combination can be properlyrealized, there can be implemented an information processing which ismore human, that is, more similar to that which is carried out within,for example, the brain of a human being.

The technique derived from the combination of the fuzzy theory and theneuron still entails a number of problems which have not been solved.For example, consider the case where A membership function capable ofdescribing the fuzziness of a known pattern is used in order to evaluatewhether or not the input pattern which is an object of recognitionmatches the reference pattern. In this case, deciding what kind ofmembership function should be selected to represent the referencepattern presents a problem.

Consider the recognition of a two-color pattern separately colored"black" and "white", by way of example. In this case, the contents ofthe membership function to be prepared must be defined differentlydepending on whether the reference pattern is "a black pattern with awhite background" or "a white pattern with a black background". If thereference pattern is "a black pattern with a white background", then amembership function which "regards white as a background" must be used.On the contrary, if the reference pattern is "a white pattern with ablack background", then a membership function which "regards white as apattern" must be used. The importance of presence or absence of defectsmuse be also taken into consideration. In this manner, for thedescription of the reference pattern to be collated with the inputpattern, the contents of the membership function used for thedescription muse be appropriately selected.

Particularly in the case where a pattern consisting of a complicated"black" portion and "white" portion is intended to be recognized, eithera large number of membership functions or a membership function having amultiplicity of peaks must be used. In addition, depending on theproperties of the reference pattern to be described, it muse be decidedwhether a membership function which "regards white as a background" or amembership function which "regards white as a pattern" is used as themembership function. Such setting would enable the recognition of acomplicated pattern.

SUMMARY OF THE INVENTION

It is a first object of the present invention to make recognition of amore complicated pattern possible.

A second object of the present invention is to enable more extensiveobjects to be recognized.

A third object of the present invention is to extend the type ofreference patterns which can be represented by membership functions.

A fourth object of the present invention is to enrich the representationof the reference patterns using the membership functions.

A pattern recognition method of the present invention comprises:

a) a first step for representing a reference pattern having fuzziness byusing a plurality of membership functions;

b) a second step for inputting an input pattern;

c) a third step for producing an inverted input pattern by logicallyinverting the input pattern;

d) a fourth step for collating the input pattern with any line of theplurality of membership functions to judge whether the input pattern isprovided with at least some of the features of the reference pattern;

e) a fifth step for collating the inverted input pattern with another ofthe membership functions to judge whether the input pattern is providedwith at least some other features of the reference pattern; and

f) a sixth step for synthesizing results of judgments in the fourth andfifth steps, and, if thus obtained result indicates that the inputpattern sufficiently matches the reference pattern, recognizing theinput pattern to be a pattern belonging to the same category as thereference pattern.

A pattern recognition method of the present invention is implemented bya device, circuit or software executing pattern matching, that is, by afuzzy neuron, based on a theory representing a reference pattern interms of membership functions which are used in the field of fuzzyinference. The present invention also employs a logical inversiontechnique for an input pattern to thereby enable various kinds ofmembership functions to be defined.

More specifically, an input pattern is collated with any one of aplurality of membership functions being defined, and, after logicalinversion thereof, is collated with another of the membership functions.Each of the membership functions is a function defining at least a partof the features of the reference pattern with fuzziness. Thus, throughmatching of the input pattern and the logically inverted input patternwith the corresponding membership function, it is judged whether or notthe input pattern is provided with at least two parts of the features ofthe reference pattern. Through this judgment if the input patternsufficiently matches the reference pattern, information can be obtainedrepresenting such a fact. In the present invention, if such informationis obtained, the input pattern will be recognized as a pattern belongingto the same category as the reference pattern.

According to the present invention, therefore, a variety of membershipfunctions can be properly defined depending on the features of thereference pattern and the objects of recognition. This ensures provisionof a means suitable for the recognition of a more complicated pattern.It will be obvious to a person of ordinary skill in the are that thiscan be applied to various objects of recognition. The representation ofthe reference pattern using the membership function or functions willalso be enriched.

In the present invention, the input of an input pattern is effectedalong a cross-detecting line which is set so as to be capable ofextracting the features of the reference pattern. The cross-detectingline is a see of sampling points, and may be a straight line or curvedline. A plurality of cross-detecting lines may be provided.

The features of the reference pattern can be grasped by the use ofconcepts of an enabling region and an inhibiting region. The enablingregion is a spatial region through which the reference pattern passes,while the inhibition region is a spatial region through which thereference pattern does not pass. If a fact that the reference patternpasses through a certain enabling region is used for the featureextraction from the input pattern, that fact is called an enablingcondition. In the same manner, if a fact that the reference pattern doesnot pass through a certain inhibiting region is used for the featureextraction from the input pattern, that fact is called an inhibitingcondition. The cross-detecting line must be set so as to cross at leasteither of the enabling region or the inhibiting region.

The membership functions capable of being defined are roughly groupedinto an enabling membership function and an inhibiting membershipfunction. The enabling membership function is a membership function forextracting, or determining, that the input pattern satisfies, in apredetermined enabling region, the enabling condition corresponding tothat region. The inhibiting membership function is a membership functionfor extracting that the input pattern satisfies, in a predeterminedinhibiting region, the inhibiting condition corresponding to thatregion. These membership functions are all multi-valued functions.

The enabling membership function can be defined as a function with aproperty presenting a maximum when the input pattern satisfies theenabling condition. On the contrary, the inhibiting membership functioncan be defined as a function with a property presenting a maximum whenthe input pattern satisfies the inhibition condition. When using theenabling membership functions and the inhibiting membership functionshaving such properties, the recognition as to whether or not the inputpattern is a pattern belonging to the same category as the referencepattern can be effected on the basis of the respective maximums of thevalues of the enabling membership functions at points on thecross-detecting line where there are obtained sampling values having apredetermined value or the inverted values of the respective maximums ofthe values of the inhibiting membership functions at such points. Inthis case, the input pattern is recognized as a pattern belonging to thesame category as the reference pattern if a minimum of the obtainedmaximums of the enabling membership functions and the inverted maximumsof the inhibiting membership functions is sufficiently large.

Moreover, a part concerning the inhibiting membership function amongsuch recognition logic can be modified by use of De Morgan's theorem.More specifically, as each of the inhibiting membership functions, afunction with a property presenting a minimum when the input patternsatisfies the inhibiting condition may be used. In order to derive therecognition results, the respective minimums of the values of theinhibiting membership function values corresponding to points on thecross-detecting line where sampling values are obtained having apredetermined value, as well as the respective maximums of the enablingmembership function values, may be used. Such types of inhibitingmembership functions are called inverted inhibiting membershipfunctions.

The inverted input pattern can also be processed by the same recognitionlogic. Since the inverted input pattern is a pattern obtained bylogically inverting the input pattern, the recognition with respect tothe inverted input pattern is substantially equal to the recognition ofa background of the pattern. Based on such an algorithm, the presentinvention realizes the recognition of a more complicated pattern.

Techniques such as logical inversion of the input pattern or thedefinition of enabling/inhibiting membership functions can accomplishrecognition more suitable for the object of recognition. For example, inthe case of the reference pattern where a plurality of enabling regionsexist along a certain cross-detecting line, a multiple-peak enablingmembership function involving all of the plurality of enabling regionsmay be used, or alternatively, a plurality of single-peak enablingmembership functions corresponding to the respective enabling regions.The alternative may depend on the object of recognition and the like.The same can be said about the reference pattern where a plurality ofinhibiting regions exist along a certain cross-detecting line.

A pattern recognition method of the present invention may be implementedas a fuzzy neuron, for example, comprising:

a) means for inputting and sampling an input pattern along across-detecting line crossing at least any one of a first enablingregion, a first inhibiting region, a second enabling region, and asecond inhibiting region;

b) means for logically inverting the input pattern to produce aninverted input pattern;

c) means for defining a first enabling membership function based on afirst enabling condition with a content that a predetermined referencepattern passes through the first enabling region; the first enablingmembership function being set so as to have its maximum within the firstenabling region:

d) means for defining a first inhibiting membership function based on afirst inhibition condition with a content that the reference patterndoes not pass through the first inhibiting region; the first inhibitingmembership function being set so as to have its maximum within the firstinhibiting region;

e) means for deriving values of the first enabling membership functionat a first set of points on the cross-detecting line where samplingvalues having a predetermined value are obtained;

f) means for deriving a maximum of the values derived by the meansrecited in e);

g) means for deriving values of the first inhibiting membership functionat the first set of points;

h) means for deriving a maximum of the values derived by the meansrecited in g);

i) means for logically inverting the maximum derived by the meansrecited in h);

j) means for defining a second enabling membership function based on asecond enabling condition with a content that a background of thereference pattern passes through the second enabling region; the secondenabling membership function being set so as to have its maximum withinthe second enabling region;

k) means for defining a second inhibiting membership function based on asecond inhibiting condition with a content that the background of thereference pattern does not pass through the second inhibiting region;the second inhibiting membership function being set so as to have itsmaximum within the second inhibiting region;

l) means for deriving values of the second enabling membership functionat a second set of points on the cross-detecting line where samplingvalues whose inverted values have the predetermined value are obtained;

m) means for deriving a maximum of the values derived by the meansrecited in l);

n) means for deriving values of the second inhibiting membershipfunction at the second set of points;

o) means for deriving a maximum of the values derived by the meansrecited in n);

p) means for logically inverting the maximum derived the means recitedin o); and

q) means for deriving a minimum value from among the maximum derived bythe means recited in f), the inverted maximum derived by the meansrecited in i), the maximum derived by the means recited in m), and theinverted maximum derived by the means recited in p);

wherein the input pattern is recognized as a pattern belonging to thesame category as the reference pattern when the minimum value derived bythe means recited in q) is sufficiently large.

Alternately, a fuzzy neuron may comprise:

a) means for inputting and sampling an input pattern along across-detecting line crossing an least any one of a first enablingregion, a first inhibiting region, a second enabling region, and asecond inhibiting region;

b) means for logically inverting the input pattern to produce aninverted input pattern;

c) means for defining a first enabling membership function based on afirst enabling condition with a content that a predetermined referencepattern passes through the first enabling region; the first enablingmembership function being set so as have its maximum within the firstenabling region;

d) means for defining a first inverted inhibiting membership functionbased on a first inhibition condition with a content that the referencepattern does not pass through the first inhibiting region; the firstinverted inhibiting membership function being see so as to have itsminimum within the first inhibiting region;

e) means for deriving values of the first enabling membership functionat a first set of points on the cross-detecting line where samplingvalues having a predetermined value are obtained;

f) means for deriving a maximum of the values derived by the meansrecited in e);

g) means for deriving values of the first inverted inhibiting membershipfunction at the first set of points;

h) means for deriving a minimum of the values derived by the meansrecited in g);

i) means for defining a second enabling membership function based on asecond enabling condition with a content that a background of thereference pattern passes through the second enabling region; the secondenabling membership function being set so as to have its maximum withinthe second enabling region;

j) means for defining a second inverted inhibiting membership functionbased on a second inhibiting condition with a content that thebackground of the reference pattern does not pass through the secondinhibiting region; the second inverted inhibiting membership functionbeing set so as to have its minimum within the second inhibiting region;

k) means for deriving values of the second enabling membership functionat a second set of points on the cross-detecting line where samplingvalues whose inverted values have a predetermined inverted value areobtained;

l) means for deriving a maximum of the values derived by the meansrecited in k);

m) means for deriving values of the second inverted inhibitingmembership function at the second set of points;

n) means for deriving a minimum of the values derived by the meansrecited in m);

o) means for deriving a minimum value from among the maximum derived bythe means recited in f), the minimum derived by the means recited in h);the maximum derived by the means recited in l), and the minimum derivedby the means recited in n);

wherein the input pattern is recognized as a pattern belonging to thesame category as the reference pattern when the minimum value derived bythe means recited in o) is sufficiently large.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates, by way of example, membership functions to bedefined when a fuzzy neuron is intended to recognize a pattern "C";

FIG. 2 is a diagram for the explanation of an enabling condition definedby an enabling membership function in FIG. 1 example;

FIG. 3 is a diagram for the explanation of an inhibiting conditiondefined by an inhibiting membership function in FIG. 1 example;

FIG. 4 is a diagram illustrating a modified example of the inhibitingmembership function shown in FIGS. 1 and 3 based on De Morgan's theorem:

FIG. 5 is a diagram showing an example of the enabling membershipfunction for the recognition of a pattern "black circle";

FIG. 6 is a diagram for explaining an erroneous recognition which maytake place when executing the judgment of degree of matching with apattern "black circle whose right edge disappears" using the enablingmembership function shown in FIG. 5;

FIG. 7 is a diagram for explaining an erroneous recognition which maytake place when executing the judgment of degree of matching with apattern "black circle a part of the interior of which is missing" usingthe enabling membership function shown in FIG. 5;

FIG. 8 is a diagram for explaining an erroneous recognition which maytake place when executing the judgment of degree of matching with apattern "black circle whose left edge disappears" using the enablingmembership function shown in FIG. 5;

FIG. 9 is a diagram illustrating, by way of example, inhibitingmembership function for the recognition of a pattern "black circle"while preventing such erroneous recognition shown in FIGS. 6 to 8;

FIG. 10 is a diagram illustrating, by way of example, an inhibitingmembership function for the recognition of a pattern "black rectangleincluding a white circle";

FIG. 11 is a diagram for the explanation of an erroneous recognitionwhich may take place when executing the judgment of degree of matchingwith a pattern "black rectangle including a white circle, the whitecircle involving a black circle therein;

FIG. 12 is a diagram illustrating an example of an enabling membershipfunction for the recognition of a pattern "black rectangle including awhite circle, the white circle permitting the presence of a black circletherein";

FIG. 13 is a diagram illustrating an example of various types ofmembership functions for recognizing a pattern "white rectangle with ablack border involving a black circle therein, the black circleincluding a white numeral 2";

FIG. 14 is a block diagram showing an overall configuration of a fuzzyneuron in accordance with a first embodiment of the present invention;

FIG. 15 is a diagram illustrating an example of various types ofmembership functions defined to have a plurality of peaks;

FIG. 16 is a diagram for explaining a conception of dividing theenabling membership function having a plurality of peaks shown in FIG.15 into a plurality of enabling membership functions each having asingle peak;

FIG. 17 is a diagram for explaining a conception of dividing theinhibiting membership function having a plurality of peaks shown in FIG.15 into a plurality of inhibiting membership functions each having asingle peak;

FIG. 18 is a diagram illustrating, by way of example, a configuration ofa comparing gate; and

FIG. 19 is a block diagram illustrating an overall configuration of afuzzy neuron in accordance with a second embodiment of the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Presently preferred exemplary embodiments of the present invention willbe described hereinbelow with reference to the accompanying drawings inwhich members having substantially the same function are designated by acommon reference numeral, and hence the description thereof will not berepeated.

Recognition Principle in Fuzzy Neuron

The following is an explanation of an example of a recognition principlein a fuzzy neuron of the present invention.

The fuzzy neuron in accordance with the present invention is intended tojudge to what degree an externally applied input pattern matches areference pattern represented by membership functions (or "categories".The representation of the reference pattern in terms of the membershipfunctions allows the reference pattern to include fuzziness, to realizea recognition processing closer to that in the human brain, or aso-called "soft" pattern matching in the fuzzy neuron of the presentinvention. The pattern matching is processing in which it is judgedwhether an externally applied input pattern sufficiently matches apredetermined pattern (which is called the reference pattern), in otherwords, whether the degree of matching is high or not to therebyrecognize the input pattern. The "soft" pattern matching means a patternmatching permitting fuzziness to some extent in the case of judgment ofthe degree of matching of the input pattern with respect to thereference pattern. Therefore, the soft matching pattern to be realizedby the fuzzy neuron may be suitable for the recognition of the inputpattern such as, for example, handwritten letters inherently includingfuzziness.

A technique which the fuzzy neuron employs to realize the "soft" patternmatching is one representing the reference pattern in terms of themembership functions. The functions are a multi-valued functionrepresenting fuzziness as is well known in the field of fuzzy processingand having a range, for example, from 0 to 1. Therefore, therepresentation of the reference pattern in terms of the membershipfunctions means imparting fuzziness to the reference pattern.

The membership functions for use in the fuzzy neuron are defined along across-detecting line. The cross-detecting line is a set of samplingpoints and is so provided as to be capable of extracting a feature orfeatures of a reference pattern having fuzziness in the form ofdistributing signals when sampling the reference pattern along thatcross-detecting line. In the fuzzy neuron, an input pattern is sampledalong the cross-detecting line to produce distributing signals for thejudgment of degree of matching through an operation based on thedistribution signals. Thus, if an applied input pattern has a feature orfeatures common to the reference pattern, then the input pattern isconsidered to properly match the reference pattern. In other words, itis recognized than the input pattern substantially conforms to thereference pattern. The cross-detecting line is not limited to a straightline, and a plurality of cross-detecting lines may be provided. It is tobe noted that the cross-detecting line must be provided in such a manneras to be capable of extracting the feature or features of a pattern tobe recognized in the form of the distributing signals which are obtainedas the result of sampling.

The membership functions to be used in the fuzzy neuron include anenabling membership function and an inhibiting membership function. Theenabling membership function is used in judging whether the appliedinput pattern satisfies an enabling condition, while the inhibitingmembership function is used to judge whether the applied input patternsatisfies an inhibiting condition. The enabling condition means acondition definitely enabling a reference pattern having fuzzinessthrough a certain region, and the inhibiting condition means a conditionnever enabling the reference pattern through a certain region. regionthrough which a reference pattern having fuzziness definitely pass iscalled an enabling region, while a region through which a referencepattern having fuzziness does non pass is called an inhibiting region.The cross-detecting line described above must be so provided as to crossat least one of the enabling regions and inhibiting regions.

By way of example, consider a handwriting pattern "C" with a blackletter on a white background as shown in FIG. 1. This pattern "C" ishandwritten and hence entails some fuzziness. In the figure, althoughthe pattern has fuzziness, such a pattern (i.e. a black letter) willpass through a region represented by a white ellipse, but will not passthrough a region represented by a hatched ellipse. In the shown example,therefore, the region represented by the white ellipse is the enablingregion, and the region represented by the hatched ellipse is theinhibiting region.

In order to ensure the recognition of an input pattern having featurescommon to the reference pattern shown in this figure, thecross-detecting line muse be provided in such a manner as is shown by abroken line, for example. Then, as seen at the bottom of FIG. 1, theenabling membership function (shown as an enabling MF) is defined inresponse to the enabling condition associated with the enabling regionrepresented by the white ellipse, while the inhibiting membershipfunction (shown as an inhibiting MF) is defined in response to theinhibiting condition associated with the inhibiting region. The enablingand inhibiting MFs must be provided with respective flat peakscorresponding to the enabling and inhibiting region, and each of thepeaks must have a predetermined width in the corresponding region torepresent the fuzziness of the reference pattern. The judgment on theenabling condition and the inhibiting condition in the fuzzy neuron canbe implemented by referring to values of the enabling membershipfunction and the inhibiting membership function based on values of thedistributing signals which are obtained along the cross-detecting line,and by subjecting the thus obtained functional values to predeterminedprocessing.

The following is a more detailed description of the judgment on theenabling condition and the inhibiting condition.

Providing that the handwritten pattern "C" shown in FIG. 1 is sampledalong the cross-detecting line shown by the broken line, then a samplevalue corresponding to "black" is obtained at a certain point within theenabling region represented by the white ellipse, whereas sample valuescorresponding to "white" are obtained across the inhibiting regionrepresented by the hatched ellipse. In the case of the example shown inFIG. 1, therefore, the enabling condition is to be capable of obtaininga sample value corresponding to "black" at a certain point within theenabling region represented by the white ellipse, and the inhibitingcondition is to be capable of obtaining sample values corresponding to"white" across the inhibiting region designated by the hatched ellipse.

Suppose that distributing signals as shown in FIG. 2 are being obtainedalong the FIG. 1 cross-detecting line particularly in the left halfthereof, when an input pattern is applied. As shown in FIG. 2, there areobtained sample values (or distributing signal values) corresponding to"black" an certain sampling points hereinbelow referred to as locations)along the cross-detecting line, and distributing signal valuescorresponding no "white" at the remaining locations. The fuzzy neuronderives a maximum vuEi of values uti of the enabling membership functionat respective locations i, where the operator v represents a maximumfunction.

If a distributing signal value corresponding to "black" is obtained atone or more locations belonging to the peak (or a part includinglocations where the enabling membership function has a value 1) of theenabling membership function, then the maximum vuEi is equal to 1. Onthe contrary, if no distributing signal values corresponding to "black"are obtained at locations belonging to the peak of the enablingmembership function, but non-zero distributing signal valuescorresponding to "black" appear at locations belonging to the foot ofthe enabling membership function, then the maximum vuEi is equal to themaximum of the non-zero distributing signal values. Accordingly, byvirtue of the above-described maximum operation, information vuEiindicating to that degree the black pattern properly passes through thepeak or the foot of the enabling membership function can be obtained. Inother words, by use of such an enabling membership function as is shownin FIG. 2, the degree of satisfaction of the enabling condition withrespect to the black pattern can be recognized. The enabling membershipfunction as shown in FIG. 2 serves to recognize the degree ofsatisfaction of the enabling condition with respect to the black patternto thereby collate the input pattern features with the reference patternfeatures and hence can be called a black-associated enabling membershipfunction or an enabling membership function with respect to black.

In the same manner, suppose that distributing signals as shown in FIG. 3are being obtained along the FIG. 1 cross-detecting line, particularlyin the right half thereof, when an input pattern is applied. There areshown obtained distributing signal values corresponding to "black" atcertain locations along the cross-detecting line, and distributingsignal values corresponding to "white" at the remaining locations. Thefuzzy neuron finds a maximum vmIi of values uIi of the inhibitingmembership function at respective locations i, and then inverts them.

If there is obtained a distributing signal value corresponding to"black" at one or more locations belonging to the peak of the inhibitingmembership function, then the inverted values of the maximum vuIi isequal to 0. On the contrary, if no distributing signal valuescorresponding to "black" are obtained at locations belonging to the peakof the inhibiting membership function, but distributing signal valuescorresponding to "black" appear at locations belonging to the foot ofthe inhibiting membership function, then inverted values of the maximumvuIi are equal to inverted values of the distributing signal valuesobtained at corresponding locations. Accordingly, through theabove-described maximum/inversion operation there can be obtainedinformation vuIi indicating the degree of "whether the black patterndefinitely does not pass through the peak or the foot of the inhibitingmembership function".

In other words, by use of such inhibiting membership function as shownin FIG. 3 there can be recognized the degree of satisfaction of theinhibiting condition with respect to the black pattern. The inhibitingmembership function as shown in FIG. 3 serves to recognize the degree ofsatisfaction of the inhibiting condition with respect to the blackpattern to thereby collate the input pattern features with the referencepattern features, and hence can be called a black-associated inhibitingmembership function or an inhibiting membership function with respect toblack.

In a case where it is judged through these processes that the enablingcondition and the inhibiting condition are sufficiently satisfied in theinput pattern, this input pattern can be considered to substantiallymatch the reference pattern.

The judgment equation of degree of matching concerning the inhibitingcondition can be modified by using de Morgan's theorem. That is, vuIican be modified as (uIi) where represents a minimum function.

Based on this fact, as shown in FIG. 4, the judgment can also beimplemented by previously inverting the inhibiting membership functionand deriving the minimum of the inverted inhibiting membership functionwith respect to the locations where "black" distributing signal valuesare obtained.

The fuzzy neuron generally executes the judgment of degree of matchingconcerning the enabling conditions and the inhibiting conditions withrespect to all the feature cross-detecting lines. From among thusobtained plural types of degree of matching, the fuzzy neuron selectsthe minimum value for output. This output value indicates to that degreethe input pattern satisfies the enabling conditions and inhibitingconditions representation of the features of the reference pattern,output value. i.e.. If the resultant degree of matching is sufficientlylarge, the input pattern can be considered to be a pattern belonging tothe same category as the reference pattern. On the contrary, if thedegree of matching is not sufficiently large, the input pattern can beconsidered to be a pattern belonging to different category from thereference pattern.

In this manner, the fuzzy neuron implements pattern recognition on thebasis of the distributing signal values obtained by sampling the inputpattern and the membership functions represent the reference pattern.The fuzzy neuron can recognize a pattern having fuzziness as it is amulti-valued function. It was impossible to carry out such recognitionthrough the conventional information processing using a binaryrepresentation.

Setting Procedure of Membership Function serving as a Premise of thePresent Invention

Deciding which color should be regarded as a pattern is a criticalproblem for setting membership functions. Assuming that the colorconsists of only white and black for simplification, this problem can berepresented as "the background is white and the pattern is black, oralternatively the background is black and the pattern is write".Depending on how to deal with this problem, that is, how to set themembership functions, the results of the judgment of degree of matchingmay differ.

For example, consider a black circle with a white background as shown inFIG. 5. Also set a cross-detecting line in such a manner as shown by abroken line in the figure. In this case, the central black circle isregarded as a pattern, and the surrounding white area is treated as abackground. Under these circumstances, it is an enabling condition to begrasped in the simplest manner that the cross-detecting line crossesthis black circle, which results in an adoption of an enablingmembership function with respect to black.

For such simple setting of the membership functions, the judgment ofdegree of matching may possibly lead to an inadequate result if an inputpattern involving white defects is applied. In the case, for example,where the right edge of the black circle disappears as shown in FIG. 6,where the black circle includes at its center a white small circle asshown in FIG. 7, or where the left edge of the black circle disappearsas shown in FIG. 8, the maximum vuEi becomes equal to 1 irrespective ofsuch defects. Therefore, it is not preferable to set the enablingmembership function as shown in FIG. 5 if the presence or absence of thewhite defects is critical.

Such inconvenience may arise from the setting of the membershipfunctions with respect to "black". Hence, in order to prevent thisinconvenience and to detect a white defect, there must be provided amembership function with respect to "white". More specifically, in is tobe grasped as an inhibiting condition that the cross-detecting linecrosses this black circle as shown in FIG. 9, and there muse be providedan inhibiting membership function with respect to "white". Then, themaximum vuIi of the inhibiting membership function is equal to 1 ifthere is a white defect present similar to that in FIG. 6. Through theinversion of this value, a degree of matching results in "0". In thismanner, membership functions should be provided with respect to white inthe case where the presence or absence of white is the criterion forrecognition.

By way of a second example, consider "a white circle in a blackrectangle" as shown in FIG. 10, and a cross-detecting line being so setas to be shown by a broken line in the figure. Provided that the blackrectangle is regarded as a pattern and than the surrounding white andthe central white circle are treated as a background in this example, itis to be grasped in the simplest manner as an inhibiting condition thatthe cross-detecting line crosses this white circle, and there isprovided a inhibiting membership function with respect to "black" asshown in the same figure.

Such simple setting of the membership function may possibly result in aninadequate value in the judgment of degree of matching if an inputpattern involving black defects is applied. In the case, for example,where a black circle exists within a white circle as shown in FIG. 11,the maximum vuIi becomes equal to 0 due to the presence of the blackcircle. Such a value is problematic if the presence or absence of theblack circle is not so essential. More specifically, it is desirable toobtain the degree of matching value of "1" irrespective of the patternas shown in FIG. 11 if only a white part has to exist at its center, andtherefore the membership function as shown in FIG. 10 is unsuitable.

Preferably, in the case of this example, there is provided an enablingmembership function with respect to white as shown in FIG. 12. Then, inspite of the presence of the black circle, the maximum vuEi becomes 1due to the presence of the white part, and hence such a membershipfunction will be preferable. That is, it is preferable to set anenabling membership function with respect to white if the presence orabsence of black defects is not essential.

Problems in Complicated Patterns

As described hereinabove, the contents of the definition of membershipfunctions that the membership function is associated with white or blackand that it is to be enabling or inhibiting may differ depending on suchcircumstances as which of white or black should be regarded as a patternor as a background, and whether the presence of defects is essential ornot in view of the object of recognition. Conversely, this means thatany complicated and high degree of pattern can be recognized through thecombination of plural kinds of membership functions. It is to be notedthat a mere application of the above-described procedure to the settingof the membership functions may lead to another problem.

For example, consider an object to be recognized as shown in FIG. 13.This is a recognition object where "there is a black border on a whitebackground, the white background extending within the black border lineand having at its center a black circle, the black circle including awhite numeral 2 therein". A cross-detecting line is provided in such amanner as is shown by a broken line in the figure, and then therecognition object is translated into membership functions in accordancewith the procedure described hereinabove. Thus there can be obtainedfour kinds of membership functions as shown in the figure.

A first membership function is one for recognizing the white numeral "2"on the black circle. This membership function is an enabling membershipfunction with respect to white with the aim of confirming of thepresence the white numeral "2" on the black circle. A second membershipfunction is one for recognizing the black circle. This membershipfunction is to be an inhibiting membership function with respect towhite in view of not permitting the presence of white defects on theblack circle. As the black circle is halved by the white numeral "2"along the cross-detecting line herein, the second membership function isto have a couple of peaks. A third membership function is one forrecognizing the white background surrounding the black circle. Thismembership function is to be an inhibiting membership function withrespect to black in view of not permitting the presence of black detectson the white background. As the white background is halved by the blackcircle along the cross-detecting line herein, the third membershipfunction is to have a couple of peaks. Finally, the fourth membershipfunction is one for recognizing the black border. This membershipfunction is no be an enabling membership function with respect to blackfor the purpose of confirming the presence of the black border. As theblack border will intersect the cross-detecting line twice herein, thefourth membership function is to have a couple of peaks.

As is apparent from the FIG. 13 example, however, more and moremembership functions must be used accordingly as the recognition objectbecomes more complicated. Furthermore, a greater number of peaks of themembership function are required accordingly as the recognition objectbecomes more complicated.

Thus, for the setting and definition of the membership functions inaccordance with the above-described procedure, the membership functionsare defined depending on such circumstances as which of white or blackis to be regarded as a pattern, and whether the defects are essential ornot. Accordingly, a more complicated object to be recognized requires amore complicated definition of the membership functions.

Details of Embodiments

Such complicated definition will be made possible by an embodiments ofthe present invention described hereinbelow. According to the followingembodiment, it becomes possible to handle a more complicated object tobe recognized and to satisfy a wider recognition object.

FIG. 14 illustrates a configuration of a fuzzy neuron in accordance witha first embodiment of the present invention. The fuzzy neuron showngenerally comprises a plurality of matching sections and a minimum valueoutput section 10. In this figure, for the purpose of simplificationonly a pair of matching sections are shown, designated at referencenumeral 1 and 2, respectively.

The matching section i includes a sensor portion 3 to be embodied in theform of, for example, a sensor array or a charge coupled device (CCD).The sensor portion 3 aces as a means for inputting an input pattern, andthe arrangement thereof constitutes a cross-detecting line therefore,output of the sensor portion 3 corresponds to the distributing signalsdescribed above. The matching section 2 which is a counterpart of thematching section 1 includes a distributing signal inverting portion 4which inverts the distributing signals received from the sensor portion3.

The matching section 1 comprises comparing gates 5-11 and 5-12, anenabling membership function definition portion 6-1, an inhibitingmembership function definition portion 7-1, maximum value outputportions 8-11 and 8-12, and an inverter 9-1. The matching section 2comprises comparing gates 5-21 and 5-22, an enabling membership functiondefinition portion 6-2, an inhibiting membership function definitionportion 7-2, maximum value output portions 8-21 and 8-22, and aninverter 9-2.

In the matching section 1, the distributing signals output from thesensor portion 3 are supplied into the comparing gates 5-11 and 5-12,respectively. The comparing gate 5-11 inputs values of an enablingmembership function defined by the enabling membership functiondefinition portion 6-1, while the comparing gate 5-12 inputs values ofan inhibiting membership function defined by the inhibiting membershipfunction definition portion 7-1. The enabling membership functiondefinition portion 6-1 and the inhibiting membership function definitionportion 7-1 may be both comprised of, for example, shift registers.

The comparing gage 5-11 compares and collates values of the enablingmembership function defined by the enabling membership functiondefinition portion 6-1 with the distributing signals supplied from thesensor portion 3, no thereby output membership function valuescorresponding to the location where the distributing signal valuesbelong to a predetermined range. For example, the comparing gate 5-11outputs the membership function values corresponding to the locationswhere input distributing signal values are "black". The comparing gate5-12 compares and collates values of the inhibiting membership functiondefined by the inhibiting membership function definition portion 7-1with the distributing values supplied from the sensor portion 3, tothereby output membership function values corresponding to the locationswhere the distributing signal value belong to a predetermined range. Forexample, the comparing gate 5-12 also outputs the membership functionvalues corresponding to the locations where input distributing signalvalues are "black".

The comparing gates 5-11 and 5-12 are followed by the maximum valueoutput portions 8-11 and 8-12, respectively. The maximum value outputportion 8-11 detects the maximum values of the membership functionvalues received from the comparing gate 5-11, and supplies them into theminimum value output portion 10. The maximum value output portion 8-12detects the maximum value of the membership function values receivedfrom the comparing gate 5-12, and supplies them into the inverter 9-1.The inverter 9-1 logically inverts thus supplied maximum value andsupplies it into the minimum output portion 10.

In the matching section 2, on the contrary, the inverted distributingsignals received from the distributing signal inverting portion 4 aresupplied into the comparing gates 5-21 and 5-22, respectively. Withinthe comparing gate 5-21 there is defined an enabling membership functionby means of the enabling membership function definition portion 6-2,while within the comparing gate 5-22 there is defined an inhibitingmembership function by means of the inhibiting membership functiondefinition portion 7-2. The enabling membership function definitionportion 6-2 and the inhibiting membership definition portion 7-2 may beboth comprised of, for example, shire registers.

The comparing gate 5-21 compares and collates values of the enablingmembership function defined by the enabling membership functiondefinition portion 6-2 with the distributing signals supplied from thedistributing signal inverting portion 4, to thereby output membershipfunction values corresponding to the locations where the distributingsignals values belong to a predetermined range. For example, thecomparing gate 5-21 outputs the membership function values correspondingto the locations where input distributing signal values are "black". Thecomparing gate 5-22 compares and collates values of the inhibitingmembership function defined by the inhibiting membership functiondefinition portion 7-2 with the distributing values supplied from thedistributing signal inverting portion 4, to thereby output membershipfunction values corresponding to the locations where the distributingsignal values belong to a predetermined range. For example, thecomparing gate 5-22 also outputs the membership function valuescorresponding to the locations where input distributing signal valuesare "black".

The comparing gates 5-21 and 5-22 are accompanied by the maximum valueoutput portions 8-21 and 8-22, respectively. The maximum value outputportion 8-21 detects the maximum value of the membership function valuesreceived from the comparing gate 5-21, and supplies it into the minimumvalue output portion 10. The maximum value output portion 8-22 detectsthe maximum value of the membership function values received from thecomparing gate 5-22, and supplies it into the inverter 9-2. The inverter9-2 logically inverts thus supplied maximum value and supplies it intothe minimum output portion 10.

The minimum value output portion 10 detects a minimum among the suppliedmaximum values or the inverted values of the maximum values, and outputsit as an output value u. The output value u indicates to what degree aninput pattern matches the reference pattern represented by themembership functions.

Accordingly, the enabling membership function to be defined by theenabling membership function definition portion 6-1 becomes an enablingmembership function with respect to black, white the inhibitingmembership function to be defined by the inhibiting membership functiondefinition portion 7-1 becomes an inhibiting membership function withrespect to black. Furthermore, since the black distributing signals areinverted into white ones and the white distributing signals are invertedinto black ones by virtue of the distributing signal inverting portion4, the enabling membership function to be defined by the enablingmembership function definition portion 6-2 becomes a enabling membershipfunction with respect to white, while the inhibiting membership functiondefined by the inhibiting membership function definition portion 7-2becomes an inhibiting membership function with respect to white. Using asimple circuit configuration in this manner a total of four kinds ofmembership functions can be defined and the judgment of degree ofmatching can be performed in this embodiment. In other words, it enablesa complicated definition of the membership functions suitable for acomplicated and high degree of object to be recognized, which mayremarkably enlarge the application of the fuzzy neuron. Although only apair of matching sections are shown in FIG. 14, the present inventionmay use three or more matching sections, and is not intended to belimited to the use of only the pair of matching sections.

In the case of providing a plurality of cross-detecting lines, forexample, it is preferable to be capable of defining four kinds ofmembership functions for each of the cross-detecting lines, and henceplural pairs of matching sections must be used. Furthermore, in order toavoid presenting a plurality of peaks as shown in FIG. 18, themembership function having a plurality of peaks must be divided into aplurality of membership functions each having a single peak. In thiscase, each of the membership functions muse be subjected to thematching, which requires plural pairs of matching sections, in dependson the object of recognition whether the membership function shouldremain with a plurality of peaks or should be divided into a pluralityof membership functions each having a single peak.

In the case where a handwritten letter "3" shown in FIG. 15 is requiredto be recognized by use of the fuzzy neuron of this embodiment, across-detecting line is provided, for example, in such a manner as shownby a broken line in the figure. When considering this case by way ofexample, it is also shown that it is possible to define an enablingmembership function having three peaks corresponding to three enablingregions and to define an inhibiting membership function having two peakscorresponding to two inhibiting regions.

However, if an applied input pattern, which belongs in a differentcategory to the reference pattern, satisfies any one of the enablingconditions corresponding to a plurality of peaks, the judgment resultwill be the same as the result obtained when the pattern belonging tothe same category with the reference pattern is input i.e. obtained inthe case where all of the peaks satisfy the enabling condition, sincethe operation for the judgment of degree of matching concerning theenabling membership function is a maximum value operation of themembership function values. Such judgment is unsuitable for the caseshown in FIG. 15 where the enabling conditions are required to besatisfied at all of the enabling regions. In order to prevent sucherroneous judgment due to the OR property of the enabling membershiphaving a plurality of peaks, the membership function having a pluralityof peaks has to be divided into a plurality of membership functions eachhaving a single peak as shown in FIG. 16.

Since the operation for the judgment of degree of matching concerningthe inhibiting membership function can be considered also as theinversion operation of the maximum of the membership function values, ifan input pattern which does non satisfy all inhibiting conditions isapplied, the judgment result will be the same as that in the case whereonly any one of the inhibiting conditions are not satisfied. In order toprevent such erroneous judgment due to the AND property of theinhibiting membership function having a plurality of peaks, themembership function having a plurality of peaks may be divided into aplurality of membership functions each having a single peak, as shown inFIG. 17.

It depends on the properties of the object to be recognized and theobject of recognition as to whether the membership function is to have aplurality of peaks or divided to have a single peak. It is thereforepreferable in general to provide a greater number of pairs of matchingsections than the number of cross-detecting lines so as to be capable ofdividedly having a single peak.

FIG. 18 illustrates a configuration of the comparing gates 5-11 to 5-22by way of example. This configuration employs transmission gates. Thisconfiguration comprises gates 5a and 5b. For the convenience ofdescription, the comparing gate 5-11 will be described as an example,but the following discussion will be applied to the other comparinggates 5-12 to 5-22 as well.

As shown in this figure, the gates 5a and 5b are interposed between anenabling membership function definition portion 6-1 which is embodied asa register for storing membership function values, and a maximum valueoutput portion 8-11. Corresponding to respective bits of the enablingmembership function definition portion 6-1, there are provided pluralpairs of gates 5a and 5b (the number of pairs corresponding to thenumber of sampling points along a cross-detecting line).

Distributing signals derived from a sensor portion 3 are input into thegates 5a and 5b by way of a terminal Z in the figure. If values of thedistributing signals input through the terminal Z are larger than apredetermined value, then the gate 5a acts to connect between X and Y.On the contrary, if values of the distributing signals input through theterminal Z are less than the predetermined value, then the gates 5a actsto disconnect X from Y. As a result, only in the case where thedistributing signal at corresponding location are sufficiently high,each bit of the membership function supplied into the maximum is valueoutput portion 8-11. The values "high" of the distributing signalscorrespond to, for example, "black".

The gate 5b acts to connect W and Y when the values of the distributingsignals input through the terminal Z are sufficiently low. The terminalW inputs a preset lower limit value which the membership function cantake. The provision of such gate 5b prevents the input into the maximumvalue output portion 8-1 from being indefinite or unstable values whenthe values of the distributing signal are sufficiently low.

FIG. 19 illustrates a configuration of a fuzzy neuron in accordance witha second embodiment of the present invention. It is to be noted thatelements identical with those in the first embodiment are designated atthe same reference numerals, and the description thereof will not berepeated.

In this embodiment, the inhibiting membership function definitionportions 7-1 and 7-2 and the maximum value output portion 8-12 and 8-22are replaced by inversion inhibiting membership function definitionportions 21-1 and 21-2 and minimum value output portions 22-1 and 22-2,respectively. The inverters 9-1 and 9-2 are not in use. This embodimentemploys (uIi) obtained through a modification of vuIi based on deMorgan's theorem.

Accordingly, this embodiment can also present the same effect as that inthe first embodiment. More specifically, it becomes possible toindependently define the enabling and inhibiting membership functionswith respect to either white or black, since inverted distributingsignal values as well as the distributing signal values are subjected tomatching with the membership function. Thus, the content ofrepresentation of the reference pattern is widened to enable therecognition of a more complicated and higher degree of pattern or therecognition for a more extensive object.

What is claimed is:
 1. An alphanumeric character recognition methodcomprising:a first step for representing a reference character havingfuzziness and comprising a plurality of features by using a plurality ofcategories, each category representing at least one feature of thereference character; a second step for inputting an input pattern; athird step for producing an inverted input pattern by logicallyinverting said input pattern; a fourth step for comparing said inputpattern with any one of said plurality of categories to make a judgmentwhether said input pattern includes at least one of the plurality offeatures of said reference character; a fifth step for comparing saidinverted input pattern with any other one of the plurality of categoriesto make a judgment whether said input pattern is provided with at leastanother one of features of said reference character; and a sixth stepfor evaluating the judgments in the fourth and fifth steps, and, if theevaluation indicates that said input pattern sufficiently matches saidreference character, recognizing that the input pattern corresponds tothe reference character.
 2. A method according to claim 1, wherein saidfirst step comprises:a step for establishing an enabling condition inwhich said reference character passes through a predetermined enablingregion; and a step for defining, as at least one of said plurality ofcategories, an enabling category having a property presenting a maximumwhen said input pattern satisfies the enabling condition; and whereinsaid second step comprises:a step for setting a cross-detecting linecrossing said enabling region; and a step for sampling said inputpattern along said cross-detecting line; and wherein said fourth stepcomprises:a step for deriving values of said enabling category at afirst set of points on said cross-detecting line where sampling valuesbelonging to a predetermined range are obtained; and a step for derivinga maximum of the values of said enabling category at the first set ofpoints; said input pattern being recognized as corresponding to thereference character in view of said enabling condition when the maximumis sufficiently large.
 3. A method according to claim 1, wherein saidfirst step comprises:a step for establishing an inhibiting condition inwhich said reference character does not pass through a predeterminedinhibiting region; and a step for defining, as at least one of saidplurality of categories, an inhibiting category having a propertypresenting a maximum when said input pattern satisfies the inhibitingcondition; and wherein said second step comprises:a step for setting across-detecting line crossing said inhibiting region; and a step forsampling said input pattern along said cross-detecting line; and whereinsaid fourth step comprises:a step for deriving values of said inhibitingcategory at a first set of points on said cross-detecting line wheresampling values belonging to a predetermined range are obtained; a stepfor deriving a maximum of the values of said inhibiting category at thefirst set of point; and a step for logically inverting the maximum; saidinput pattern being recognized as corresponding to the referencecharacter in view of said inhibiting condition when said logicallyinverted maximum is sufficiently large.
 4. A method according to claim1, whereinsaid first step comprises:a step for establishing aninhibiting condition in which said reference character does not passthrough a predetermined inhibiting region; and a step for defining, asat least one of said plurality of categories, an inverted inhibitingcategory having a property presenting a minimum when said input patternsatisfies the inhibiting condition; and wherein said second stepcomprises:a step for setting a cross-detecting line crossing saidinhibiting region; and a step for sampling said input pattern along saidcross-detecting line; and wherein said fourth set comprises:a step forderiving values of said inverted inhibiting category at a first set ofpoints on said cross-detecting line where sampling values belonging to apredetermined range are obtained; and a step for deriving a minimum ofthe values of said inverted inhibiting category at the first set ofpoints; said input pattern being recognized as corresponding to thereference character in view of said inhibiting condition when theminimum is sufficiently large.
 5. A method according to claim 1, whereinsaid first step comprises:a step for establishing an enabling conditionin which a background of said reference character passes through apredetermined enabling region; and a step for defining, as at least oneof said plurality of categories, an enabling category having a propertypresenting a maximum when said inverted input pattern satisfies theenabling condition; and wherein said second step comprises:a step forsetting a cross-detecting line crossing said enabling region; and a stepfor sampling said input pattern along said cross-detecting line; andwherein said fifth step comprises:a step for deriving values of saidenabling category at a second set of points on said cross-detecting linewhere sampling values belonging to a predetermined range are obtained;and a step for deriving a maximum of the values of said enablingcategory of the second set of points; said input pattern beingrecognized as corresponding to the reference character in view of saidenabling condition when the maximum is sufficiently large.
 6. A methodaccording to claim 1, wherein said first step comprises:a step forestablishing an inhibiting condition in which a background of saidreference character does not pass through a predetermined inhibitingregion; and a step for defining, as at least one of said plurality ofcategories, an inhibiting category having a property presenting amaximum when said inverted input pattern satisfies the inhibitingcondition; and wherein said second step comprises:a step for setting across-detecting line crossing said inhibiting region; and a step forsampling said input pattern along said cross-detecting line; and whereinsaid fifth step comprises:a step for deriving values of said inhibitingcategory at a second set of points on said cross-detecting line wheresampling values belonging to a predetermined range are obtained; a stepfor deriving a maximum of the values of said inhibiting category at thesecond set of points; and a step for logically inverting the maximum;said input pattern being recognized as corresponding to the referencecharacter in view of said inhibiting condition when said logicallyinverted maximum is sufficiently large.
 7. A method according to claim1, wherein said first step comprises:a step for establishing aninhibiting condition in which a background of said reference characterdoes not pass through a predetermined inhibiting region; and a step fordefining, as at least one of said plurality of categories, an invertedinhibiting category having a property presenting a minimum when saidinverted input pattern satisfies the inhibiting condition; and whereinsaid second step comprises:a step for setting a cross-detecting linecrossing said inhibiting region; and a step for sampling said inputpattern along said cross-detecting line; and wherein said fifth stepcomprises:a step for deriving values of said inverted inhibitingcategory at a second set of points on said cross-detecting line wheresampling values having a predetermined value are obtained; and a stepfor deriving a minimum of the values of said inverted inhibitingcategory at the second set of points; and said input pattern beingrecognized as corresponding to the reference character in view of saidinhibiting condition when the minimum is sufficiently large.
 8. A methodaccording to claim 1, whereinsaid first step includes:a step forestablishing (i) a first enabling condition in which said referencecharacter passes through a predetermined first enabling region, (ii) afirst inhibiting condition in which said reference character does notpass through a predetermined first inhibiting region, (iii) a secondenabling condition in which a background of said reference characterpasses through a predetermined second enabling region, and (iv) a secondinhibiting condition in which the background of said reference characterdoes not pass through a predetermined second inhibiting region; and astep for defining, as said plurality of categories, a first enablingcategory having a property presenting a maximum when said input patternsatisfies said first enabling condition, a first inhibiting categoryhaving a property presenting a maximum when said input pattern satisfiessaid first inhibiting condition, a second enabling category having aproperty presenting a maximum when said inverted input pattern satisfiessaid second enabling condition, and a second inhibiting category havinga property presenting a maximum when said inverted input patternsatisfies said second inhibiting condition; and wherein said second stepcomprises:a step for setting a cross-detecting line crossing said firstenabling region, said first inhibiting region, said second enablingregion, and said second inhibiting region; and a step for sampling saidinput pattern along said cross-detecting line; and wherein said fourthstep comprises:a step for deriving values of said first enablingcategory and said first inhibiting category at a first set of points onsaid cross-detecting line where sampling values belonging to the firstpredetermined range are obtained; a step for deriving a maximum of thevalues of said first enabling category at the first set of points; astep for deriving a maximum of the values of said first inhibitingcategory at the first set of points; and a step for logically invertingthe maximum of said first inhibiting category at the first set ofpoints; and wherein said fifth step comprises:a step for deriving valuesof said second enabling category and said second inhibiting category ata second set of points on said cross-detecting line where samplingvalues whose inverted values belong to the second predetermined rangeare obtained; a step for deriving a maximum of the values of said secondenabling category at the second set of points; a step for deriving amaximum of the values of said second inhibiting category at the secondset of points; and a step for logically inverting the maximum of saidsecond inhibiting category at the second set of points; and wherein saidsixth step comprises:a step for deriving a minimum from among themaximum of said first enabling category, the inverted maximum of saidfirst inhibiting category, the maximum of said second enablingcategories, and the inverted maximum of said second inhibiting categoryvalues, and a step for outputting the minimum as a value that indicateswhether said input pattern sufficiently matches said referencecharacter; said input pattern being recognized as corresponding to thereference pattern when said output minimum value is sufficiently large.9. A method according to claim 1, wherein said first step comprises:astep for establishing a first enabling condition in which said referencecharacter passes through a predetermined first enabling region, a firstinhibiting condition in which said reference character does not passthrough a predetermined first inhibiting region, a second enablingcondition in which a background of said reference character passesthrough a predetermined second enabling region, and a second inhibitingcondition in which the background of said reference character does notpass through a predetermined second inhibiting region; and a step fordefining, as said plurality of categories, a first enabling categoryhaving a property presenting a maximum when said input pattern satisfiessaid first enabling condition, a first inverted inhibiting categoryhaving a property presenting a minimum when said input pattern satisfiessaid first inhibiting condition, a second enabling category having aproperty presenting a maximum when said inverted input pattern satisfiessaid second enabling condition, and a second inverted inhibitingcategory having a property presenting a minimum when said invertedpattern satisfies said second inhibiting condition; and wherein saidsecond step comprises:a step for setting a cross-detecting line crossingsaid first enabling region, said first inhibiting region, said secondenabling region, and said second inhibiting region; and a step forsampling said input pattern along said cross-detecting line; and whereinsaid fourth step comprises:a step for deriving values of said firstenabling category and said first inverted inhibiting category at a firstset of points on said cross-detecting line where sampling valuesbelonging to a first predetermined range are obtained; a step forderiving a maximum of the values of said first enabling category at thefirst set of points; and a step for deriving a minimum of the values ofsaid first inverted inhibiting category at the second set of points;said fifth step comprises:a step for deriving values of said secondenabling category and said second inverted inhibiting category at asecond set of points on said cross-detecting line where there areobtained sampling values whose inverted values belong to a secondpredetermined range; a step for deriving a maximum of the values of saidsecond enabling category at the second set of points; and a step forderiving a minimum of the values of said second inverted inhibitingcategory at the second set of points; said sixth step comprises:a stepfor deriving a minimum as an output value from among (i) the maximum ofsaid first enabling category; (ii) the minimum of said first invertedinhibiting category, (iii) the maximum of said second enabling category,and (iv) the minimum of said second inverted inhibiting category, and astep for outputting the output value as a value that indicates whethersaid input pattern sufficiently matches said reference character; saidinput pattern being recognized as corresponding to the referencecharacter when said output value is sufficiently large.
 10. A methodaccording to claim 1, whereinsaid second step includes a step forinputting said input pattern along a cross-detecting line being set soas to cross a plurality of regions where features of said referencecharacter exist; and whereinsaid first step includes a step forrepresenting, by a single category, a plurality of regions wherefeatures having a common property among said plurality of regions exist;said single category being a multi-valued function having a plurality offlat peaks with two feet.
 11. A method according to claim 1, whereinsaid second step includes a step for inputting said input pattern alonga cross-detecting line which is set so as to cross a plurality ofregions where features of said reference character exist; andwhereinsaid first step includes a step for representing, by a pluralityof different categories, a plurality of regions where features having acommon property among said plurality of regions exist; each of saidplurality of categories being a multi-valued function having a singleflat peak with two feet.
 12. A method for recognizing an alphanumericcharacter comprising:generating a plurality of categories collectivelyrepresenting a reference character having identifying characteristics,each category representing at least one identifying characteristic ofthe reference character; scanning an input character using a sensordevice to generate an input pattern representative of the inputcharacter; transforming the input pattern to generate an inverted inputpattern; comparing the input pattern with a first category to determinea first quantity of identifying characteristics of the referencecharacter that are present in the input character; comparing theinverted input pattern with a second category to determine a secondquantity of identifying characteristics of the reference character thatare present in the input character; and recognizing that the inputcharacter matches the reference character if the first and secondquantities of identifying characteristics are sufficiently high.